# Rotation

A rotation of a planar figure is a transformation that preserves area and angles, but not orientation. The resulting figure is congruent to the first.

Suppose we wish to rotate triangle clockwise around a point , also known as the **center of rotation**.

We would first draw segment . Then, we would draw a new segment, such that the angle formed is , and . Do this for points and , to get the new triangle

### Practice Problems

- Isosceles has a right angle at . Point is inside , such that , , and . Legs and have length , where and are positive integers. What is ?

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- Suppose that is an equilateral triangle of side length , with the property that there is a unique point inside the triangle such that , , and . What is ?

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- Three concentric circles have radii and An equilateral triangle with one vertex on each circle has side length The largest possible area of the triangle can be written as where and are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find

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